Coherent radiation in the range from soft X-rays up to hard X-rays, produced by the low-emittance electron beam of MAMI, can be used for various applications. Novel types of interferometers have been developed for the measurement of the complex index of refraction of thin self-supporting foils. For the vacuum ultraviolet and soft X-ray region the interferometer consists of two collinear undulators, and a grating spectrometer. A foil placed between the undulators causes a phase shift and an attenuation of the oscillation amplitude. The complex index of refraction has been measured at the L 2,3-absorption edges of nickel. A novel method is described for the measurement of the X-ray magnetic circular birefringence. For the hard X-ray region the interferometer consists of two foils at which the 855 MeV electron beam produces transition radiation. Distinct interference oscillations have been observed as a function of both, the photon emission angle and the distance between the foils. The refractive index decrement δ(ω) of a 2 µm thick nickel sample foil has been measured at X-ray energies around the K absorption edge at 8333 eV and at 9930 eV with an accuracy of better than 1.5 %. The line width of parametric X radiation (PXR) was measured in backward geometry with a Si single-crystal monochromator. Upper limits of the line width of 42meV, 50meV, and 44meV, have been determined for the (333), (444) and (555) reflections at photon energies of 5932 eV, 7909 eV, and 9887 eV, respectively. Small angle scattering of the electrons in the crystal leads to a stochastic frequency modulation of the exponentially damped wave train which results in the line broadening. To elucidate the quest if the production of PXR is a kinematical or a dynamical process the radiation from silicon single-crystal targets, emitted close to the electron direction, has been studied. The observed interference structures and the narrow-band radiation in forward direction shows that PXR is produced in a dynamical process.
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